How can I quickly decide the longest-wavelength line in a hydrogen spectral series?
Within one named series, the final level n_f is fixed.
Within one named series, the final level n_f is fixed. Since photon energy hc/lambda equals the level difference, longest wavelength means the smallest possible energy difference. That occurs for the nearest allowed upper level, n_i = n_f + 1. The series limit n_i = infinity gives the largest energy difference and therefore the shortest wavelength, not the longest.
Key point
Longest wavelength: smallest adjacent drop; series limit: shortest wavelength.
Common mistake
choosing n_i = infinity for the longest wavelength.
Memory tip
small energy gap means long wave.
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